Approximation processes arise in a very natural way in many problems dealing with the constructive approximation of functions as well as solutions to (partial) differential equations and integral equations. The study of such subject falls into an intensive research area, developing in different directions by many mathematicians. Several investigations have been devoted to the approximation properties of new sequences of operators, which might generalize or modify well-known ones, in order to get better results. Issues related to these studies are, for instance, shape preserving properties of the approximating operators, estimates of the rate of convergence, asymptotic formulae, saturation problems, approximation of semigroups of operators, asymptotic behavior, direct, and converse results. Several approximation processes have been successfully applied for example in Computer Aided Geometric Design, in the theory of artificial neural networks, and in evolution problems arising in population genetics, financial mathematics, and other fields.

The goal of this special issue is to attract original research as well as review articles that highlight recent advances in operator methods in approximation theory and related applications.

Potential topics include but are not limited to the following:

• Approximation by positive operators
• Approximation by linear/nonlinear operators
• Approximation by integral operators
• Rate of convergence and moduli of smoothness
• Simultaneous approximation
• Approximation problems for semigroups of operators and evolution equations
• Multidimensional problems
• Abstract approximation theory
• Quantum Calculus in Approximation Theory